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1.
In this paper, a new method is presented based on [1]. It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived. The convergence of the solution is proved. Finally, it is only necessary to solve a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resullants and displacements can be obtained by the present method. The correctness of the theory in this paper is, confirmed. 相似文献
2.
Only the electron and ion gases were taken into account in all previous theories of the positive column of intermediately-low-pressure
arc discharge with or without the longitudinal magnetic field, while the motion of neutral gas was neglected. In 1982, the
authors[1] presented a nonlinear theory of a positive column which indicated that the rotating velocities of neutral gas and ion gas
were nearly equal, and the motion of neutral gas could not be ignored. They further discussed the problem of validity of Bohm's
criterion. However, some of the parameters with which the computation was worked out in Ref. [1] were not correlated to the
initial discharge parameters. In the present paper, two integral relations are supplemented, so that a complete mathematical
formation of the problem is given. A convergent numerical solution is obtained by iteration and the solution of Ref. [1] turns
out to be the first iteration approximation. It is shown that both functions and parameters obtained by self-consistent solution
differ significantly from those obtained in the first iteration approximation. According to this paper the computation can
be conducted when the initial discharge parameters are given, so this method could have certain practical applications. 相似文献
3.
RBF神经网络及其在结构损伤识别中的应用研究 总被引:12,自引:0,他引:12
采用具有更好的仿生效果的径向基函数(RBF)网络对单处损伤结构及多处损伤结构的损伤程度,位置,区域,处数进行识别,网络学习方法选择了简单易行,精度高且运算速度快的正交最小二乘(OLS)法,通过实例对该方法进行了测试,并与BP网进行了比较,测试结果可验证:RBF网络及其OLS学习方法可以快速,有效,高精度地识别结构损伤状况。 相似文献
4.
In this paper,a new method,exact element method for constructing finite element,ispresented.It can be applied to solve nonpositive definite or positive definite partialdifferential equation with arbitrary variable coefficient under arbitrary boundarycondition.Its convergence is proved and its united formula for solving partial differentialequation is given.By the present method,a noncompatible element can be obtained and thecompatibility conditions between elements can be treated very easily.Comparing the exactelement method with the general finite element method with the same degrees of freedom,the high convergence rate of the high order derivatives of solution can be obtained.Threenumerical examples are given at the end of this paper,which indicate all results canconverge to exact solution and have higher numerical precision. 相似文献
5.
纪振义 《应用数学和力学(英文版)》1988,9(12):1183-1193
The step reduction method was first suggested by Prof. Yeh Kai-yuan[1]. This method has more advantages than other numerical methods. By this method, the analytic expression of solution can he obtained for solving nonuniform elastic mechanics. At the same time, its calculating time is very short and convergent speed very fast. In this paper. the convergent condition and united formula of step reduction method are given by mathematical method. It is proved that the solution of displacement and stress resultants obtained by this method can converge to exact solution uniformly. when the convergent condition is satisfied. By united formula, the analytic solution can be expressed as matrix form, and therefore the former complicated expression can be avoided. Two numerical examples are given at the end of this paper which indicate that by the theory in this paper, a right model can be obtained for step reduction method.Project Supported by Science and Technic Fund of the National Education Committee.The author would like to thank Prof. Yeh Kai-yuan for his directing. 相似文献
6.
本文在文[1]和文[2]的基础上,提出构造非协调有限元的新方法。该方法不用一般的变分原理,可适用任意变系数正定和非正定偏微分方程。利用这一方法得到一个新的八节点四边形平面应力单元。与一般有限元相比,位移和应力可提高一阶收敛精度。形成单刚矩阵时,不需要进行数值积分。单元之间的协调条件容易满足,文中给出收敛性证明。文末给出数值算例,表明利用本文的方法,应力和位移均可获得满意的数值精度。 相似文献
7.
本文利用[1]的方法,构造了一个九节点非协调三角形平面单元.与一般有限元相比可以提高一阶收敛精度,应力可直接在单元节点上得到.形成单刚矩阵时,不需要在单元域内进行数值积分,容易构造曲边单元.文末的算例表明,仅用很少的单元,位移和应力即可获得较高的精度. 相似文献
8.
基于含椭圆核有限大各向异性板弹性问题的复变函数级数解,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元.单元内的应力场和位移场采用满足平衡方程、几何方程与物理方程的复变函数级数解,假设的复变函数级数解精确满足椭圆核边界处的位移协调条件和应力连续条件,单元外边界上的位移场按常规有限元位移场假设,单元内椭圆核的长轴可以与材料主轴不重合.单元刚度矩阵采用Gauss积分求得,并给出了建立刚度矩阵的主要公式和推倒过程.数值计算结果表明该单元具有计算精度高、计算工作量小等优点. 相似文献
9.
连续时间线性约束LQ控制问题的时程精细积分方法 总被引:1,自引:0,他引:1
本文基于连续时间线性约束LQ控制问题,给出时段的消元公式。由于消元过程与消元次序无关,故可在此过程中引入2N类高精度时程积分方法,求出Riccati方程后,对状态向量进一步采用时程精细积分法,可确定系统非常精确的状态向量,该方法不仅保证了系统的计算精度,而且有很好的数值稳定性,数值例题说明了本文方法的有效性。 相似文献
10.
11.
Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation format is obtained. Its convergence is proved. We can get analytic expressions which converge to exact solution and its higher order derivatives unifornuy. Four numerical examples are given, which indicate that satisfactory results can be obtained by this method. 相似文献
12.
发展了一种研究叶轮机内动、静叶间的相互作用的新方法———扰动涡方法,它利用全三维的定常解为基础解,并由此给出非定常扰动场的初始解.为计算叶片对扰动场的响应过程,采用拉格朗日方法追踪扰动涡团的对流流动过程,用确定性涡方法来描述流体的粘性扩散过程.发展了代数湍流模型(Baldwin Lomax湍流模型)在尾迹中的应用方法,克服了其它数值方法中无法准确捕捉尾迹中心线的运动轨迹,以及计算出的边界层外的湍流涡粘性系数偏大的缺陷.利用该方法计算轴流叶轮机内由于动、静叶间的相互作用而引起的非定常流动过程,与实验的对照表明,模拟结果与实验数据吻合得相当好,从而说明本文发展的方法是可信的,为更直观地描述尾迹等非定常因素的流动及叶轮机内的掺混问题提供依据. 相似文献
13.
A new finite element analysis principle based on neural networks is propsed. It can realize the finite element analysis in
real time. The neural computation of a simple structure was simulated on digital computer, the effect of input parameters
on convergent speed and precision was analyzed. Before solving a certain FE problem, the linking weight matrix of the neural
net, i.e., the global stiffness matrix of the structure analyzed, must be defined. In this paper, a method which uses the
BP net to compute the element stiffness matrix in real time is proposed.
The subject is supported by the Natural Science Foundation of China 相似文献
14.
乔宗椿 《应用数学和力学(英文版)》1993,14(10):953-962
In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well. 相似文献
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17.
This paper presents a new curved quadrilateral plate element with12-degree freedom by the exact element method.The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle.Using this method,the compatibility conditions between element can be treated very easily,if displacements and stress resultants are continuous at nodes between elements.The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed.Numerical examples are given at the end of this paper,which show the excellent precision and efficiency of the new element. 相似文献
18.
In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method. 相似文献
19.
In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn ’t need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi ’s transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes. 相似文献
20.
本文在双连杆空间柔性机械臂系统非线性动力学方程的基础上,运用线性二次型(LQ)最优控制方法讨论了机械臂消除残余振动的控制问题。本文重点在于系统计算过程中,放弃了传统的差分类算法,对时变控制系统,引入时程精细积分方法,由于精细积分方法在有限的时间步长内又进行了更精细的划分,同时避免了差分法的许多计算障碍,使得该计算方法具有计算精度高及数值计算无条件稳定等特点。文中针对双连杆空间柔性机械臂系统这一典型结构,给出了其精细控制律,以说明精细积分法的优越性。 相似文献